Preheat the oven to 400°F (205°C). Line a rimmed baking sheet with parchment paper.
Unfold the puff pastry on a floured cutting board and gently press out any wrinkles.
Using a 4-inch (10cm) flower-shaped, scalloped, or circular cookie cutter, cut out 4 rounds. Arrange the dough rounds on the baking sheet.
In a small bowl, stir together the brown sugar, butter, salt, and 1 teaspoon of the cinnamon. Divide the mixture evenly among the dough rounds, mounding in the center.
Cut the pears into 1/8-inch (3-mm) slices, leaving the stem end attached. Fan out the cut ends of the pears as you place them cored-side down on the dough rounds, covering the butter mixture.
In a small bowl, stir together the granulated sugar and remaining 1/4 teaspoon cinnamon. Sprinkle the cinnamon-sugar mixture over the pears.
Bake until the pastry is puffed and browned, 18 to 20 minutes.
Remove the tarts from the oven. Cool for 10 minutes. Serve warm.